CN113804148A - Measuring adjustment method based on dynamic reference - Google Patents

Measuring adjustment method based on dynamic reference Download PDF

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CN113804148A
CN113804148A CN202110891913.7A CN202110891913A CN113804148A CN 113804148 A CN113804148 A CN 113804148A CN 202110891913 A CN202110891913 A CN 202110891913A CN 113804148 A CN113804148 A CN 113804148A
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foundation pit
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CN113804148B (en
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王晓光
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Jilin University of Architecture and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
    • E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
    • E02D33/00—Testing foundations or foundation structures

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Abstract

The invention discloses a measuring adjustment method based on a dynamic datum, which relates to the technical field of building measurement.A plurality of datum points and observation points are arranged in a foundation pit to be monitored, and the datum points are arranged in a curve manner, wherein the datum points are arranged at the edge of the foundation pit; setting a reference point coordinate, and calculating by combining the direction angle and the distance between the reference point and the observation point and combining a gravity center coordinate and a difference method to obtain a coordinate of the observation point; when the foundation pit deforms, a plurality of deformed reference points are obtained, the coordinates of the deformed reference points are obtained according to the coordinates of the observation points, the distance and the direction value between the observation points and the arbitrarily selected deformed reference points are combined, the least square method is combined, the coordinates of the deformed reference points are calculated and obtained, the deformed reference coordinates and the reference coordinates in S1 are calculated, and the foundation pit displacement value is calculated. The invention solves the problem of calculating the movement amount of the foundation pit deformation monitoring point by methods of barycentric coordinates, least squares and the like.

Description

Measuring adjustment method based on dynamic reference
Technical Field
The invention relates to the technical field of building measurement, in particular to a measurement adjustment method based on a dynamic reference.
Background
The construction of subways, underground light rails, underground stations and underground parking lots all comprises a deep foundation pit construction link. In the process of digging the deep part of the foundation pit, the deformation observation of the edge support of the foundation pit is regularly carried out, and the deformation observation is a specified measuring link in the process of constructing the foundation pit. The foundation pit engineering is often located in urban building dense areas, and it is very difficult to set a reference point for deformation measurement outside the deformation range of the foundation pit, so the foundation pit deformation monitoring is often without reference. . Therefore, the invention provides a dynamic reference-based adjustment measurement method, which solves the problem of calculation of the movement amount of the foundation pit deformation monitoring point through a virtual reference and a least square approximation method.
Disclosure of Invention
In view of the above technical shortcomings, the present invention provides a dynamic reference-based measurement adjustment method.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a measurement adjustment method based on dynamic reference comprises the following steps:
s1, arranging a plurality of datum points and observation points in the foundation pit to be monitored, wherein the datum points are arranged on the edge of the foundation pit in a curve manner;
s2, setting a reference point coordinate, and calculating to obtain the coordinate of the observation point by combining the direction angle and the distance between the reference point and the observation point and combining the gravity center coordinate and a difference method;
s3, when the foundation pit deforms, obtaining a plurality of deformed reference points, obtaining coordinates of the deformed reference points according to coordinates of the observation points, combining the distance and direction values of the observation points and the arbitrarily selected deformed reference points, combining a least square method, calculating to obtain coordinates of the deformed reference points, calculating to obtain the deformed reference coordinates and the reference coordinates in S1, and calculating a foundation pit displacement value.
Preferably, the observation point calculation process described in step S2 is as follows:
approximate coordinates in an arbitrary coordinate system: x is the number ofi″,yi″,i＝1,2,‥‥,n；
Direction observation value: l isi，i＝1,2,‥‥,3n；
Distance observation value: di，i＝1,2,‥‥,3n；
Obtaining a balance value by a balance method:
xi′＝xi″+δxi
yi′＝yi″+δyi
barycentric coordinates of the reference points:
Figure BDA0003196480440000021
Figure BDA0003196480440000022
in the formula: n is the number of points;
the barycentric coordinates of the reference points to the azimuth angle of the set reference points:
Figure BDA0003196480440000023
the center of gravity coordinates of the observation points are equal to the reference center of gravity coordinates:
xc＝Xc
yc＝Yc
the azimuth angle from the barycentric coordinate of the observation point to the set observation point is equal to the azimuth angle from the barycentric coordinate of the reference point to the set reference point:
α′c1＝αc1
obtaining the coordinates of the observation points:
Figure BDA0003196480440000024
preferably, the adjustment method specifically calculates as follows:
directional observation error equation:
vLi＝-δZ0+αiδx0+biδy0-aiδxi-biδyi-li
in the formula: a isi，biAre respectively the linearized coefficient, δx0，δy0Two translational amounts, δ, each being a dynamic referenceZ0A rotation amount that is a dynamic reference; distance observation error equation:
vDi＝-cosαiδx0-sinαiδy0+cosαiδxi+sinαiδyi-lDi
in the formula: 12 … m, lDiIs a constant term, δx0、δy0Are respectively observation points, δxi，δy0Respectively as a sight point;
in the formula: 12 … 3 n;
coefficients of the normal equation:
NBB＝BT·P·B
in the formula: delta is a vector, B is a row vector, and l is a constant term;
constant term of the normal equation:
W＝BT·P·l
in the formula: b isTIs matrix transposition, P is a weight matrix, and B is a matrix without transposition;
the equation:
NBBδ-W＝0
obtaining:
NCCδ-W＝0
obtaining a balance value:
xi′＝xi″+δxi
yi′＝yi″+δyi。
preferably, the specific calculation process in step S3 is as follows:
the amount v of deformation of the deformed reference point in the X direction and the Y directionxi，vyiRespectively as follows:
Figure BDA0003196480440000031
obtaining according to a least square method:
Figure BDA0003196480440000032
Figure BDA0003196480440000033
Figure BDA0003196480440000034
obtaining a foundation pit displacement value:
Figure BDA0003196480440000035
in the formula: δ is the vector, B is the row vector, and l is the constant term.
Preferably, in step S1, a plurality of reference points are disposed at the edge of the foundation pit to be monitored, and the plurality of reference points may be distributed in a hyperbolic curve at the edge of the foundation pit to be monitored.
The invention has the beneficial effects that: the invention solves the problem of foundation pit displacement calculation through methods such as barycentric coordinates, least squares and the like.
Drawings
FIG. 1 is a diagram of datum layout provided by the present invention;
FIG. 2 is a view of the present invention providing a deformed foundation pit;
FIG. 3 is a simplified datum point deformation provided by the present invention;
fig. 4 is a schematic flow chart provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the accompanying drawings, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
In order to measure the deformation of the edge of the foundation pit generated along with the excavation depth of the foundation pit, n forced centering points are established on the foundation pit edge support to serve as deformation monitoring points.
And arranging two or more total station free measuring stations in the foundation pit, and carrying out full circle direction observation and distance observation on the deformation monitoring points. Arbitrarily assuming the coordinates of a point and the azimuth angle of a side, a set of coordinates x of all points in the arbitrary coordinate system is measuredi″,yi", is a rough coordinate in the case of adjustment.
In order to make the adjustment result have uniform precision, the adjustment of the coordinates of the corner free net is carried out in rank deficiency. Obtaining a group of even coordinate values x with uniform precision in any coordinate systemi′,yi′。
Using the coordinate of a deformation point (or the coordinate of the deformation point obtained by observing the previous deformation) X before excavation of the foundation piti,YiAs a reference for deformation amount calculation of the deformation point.
And (4) a coordinate system is unified by using a gravity center point coordinate and a ray coincidence method.
The relative position between the reference and the current deformation point in the same coordinate system is incorrect, and the correct deformation amount of the displacement point relative to the reference cannot be obtained. Stipulating: the position of the deformation monitoring point is fixed and unchanged, and the benchmark is in a free state on the premise of ensuring that the relative position relation of each element is unchanged, and the benchmark is called as a dynamic benchmark. And determining the correct position of the reference according to the least square principle, and solving the displacement of the deformation point.
As shown in fig. 1, the observed value
Observed value of A survey station
Figure BDA0003196480440000041
Figure BDA0003196480440000051
Figure BDA0003196480440000061
Observed value of B measuring station
Figure BDA0003196480440000071
Figure BDA0003196480440000081
The center of gravity is not changed
Rank deficient corner free net adjustment
Known data are:
approximate coordinates in an arbitrary coordinate system: x is the number ofi″,yi″,i＝1,2,‥‥,n；
Direction observation value: l isi，i＝1,2,‥‥,3n；
Distance observation value: di，i＝1,2,‥‥,3n；
Weight of observed value:
σ0＝σL＝σ0＝σL＝±2″
σDi＝±(1+1Dippm)mm
PLi＝1
Figure BDA0003196480440000091
approximation calculation
Error equation:
directional observation error equation:
vLi＝-δZ0+αiδx0+biδy0-aiδxi-biδyi-li
distance observation error equation:
vDi＝-cosαiδx0-sinαiδy0+cosαiδxi+sinαiδyi-lDi
i＝1 2…3n；
namely:
Figure BDA0003196480440000092
the formula of the composition method is as follows:
coefficients of the normal equation:
NBB＝BT·P·B
constant term of the normal equation:
W＝BT·P·l
the equation:
NBBδ-W＝0
establishing a reference constraint condition:
SSTδ＝0
setting:
NCC＝NBB+SST
obtaining:
NCCδ-W＝0
solving equation to obtain:
Figure BDA0003196480440000101
the adjustment value is as follows:
xi′＝xi″+δxi
yi′＝yi″+δyi
the adjustment coordinate value of the measurement
Point number xi′ yi′
"1" 6047.3747 8583.6418
"2" 6056.293 8594.6644
"3" 6061.1936 8608.7845
"4" 6061.7616 8623.3452
"5" 6058.55 8637.8163
"6" 6053.7066 8648.2483
"7" 6047.5005 8656.9186
"8" 6040.6334 8663.8962
"9" 6032.6807 8668.8475
"10" 6024.1245 8671.9461
"11" 6016.3661 8673.333
"12" 6005.9727 8671.9547
"13" 5996.0637 8666.2083
"14" 5989.2708 8658.8569
"15" 5984.5244 8647.3368
"16" 5982.6248 8636.4767
"17" 5983.5539 8624.818
"18" 5987.0029 8611.7045
"19" 5992.5727 8600.2622
"20" 6000.7462 8590.6643
"21" 6009.6837 8582.9776
"22" 6021.2546 8578.0571
"23" 6035.1319 8578.3272
Reference coordinate Xi,Yi
Point number Reference Xi Reference Yi
"1" 6004.6936 8442.856
"2" 6016.8197 8450.2088
"3" 6026.2131 8461.8364
"4" 6031.6784 8475.345
"5" 6033.5571 8490.0506
"6" 6032.5323 8501.5072
"7" 6029.6289 8511.7669
"8" 6025.5299 8520.6586
"9" 6019.7231 8528.0114
"10" 6012.7207 8533.8252
"11" 6005.8891 8537.7581
"12" 5995.6417 8539.9811
"13" 5984.3696 8537.9291
"14" 5975.4886 8533.3123
"15" 5967.1199 8524.0785
"16" 5961.6546 8514.5028
"17" 5958.5804 8503.2172
"18" 5957.3848 8489.7086
"19" 5958.7512 8477.055
"20" 5963.1917 8465.2563
"21" 5968.9985 8454.9966
"22" 5978.2212 8446.4469
"23" 5991.372 8442.001
Calculating barycentric coordinates of the reference:
Figure BDA0003196480440000131
Figure BDA0003196480440000132
calculating the azimuth angle from the reference gravity center to the reference point No. 1:
Figure BDA0003196480440000133
and calculating the barycentric coordinates of the measurement:
Figure BDA0003196480440000134
Figure BDA0003196480440000135
calculating the distance and the azimuth angle from the gravity center point to each observation point ray in the measurement:
Figure BDA0003196480440000136
Figure BDA0003196480440000137
and (3) calculating an included angle of adjacent rays:
βi＝α′ci+1-α′ci
calculating the current observation coordinate in the reference circle:
the observation points should be numbered the same as the corresponding reference points, and should be numbered clockwise,
the center of gravity coordinates of the observation points are equal to the reference center of gravity coordinates:
xc＝Xc
yc＝Yc
the azimuth angle from the observation gravity center point to observation point No. 1 is equal to the azimuth angle from the reference gravity center point to reference point No. 1.
α′c1＝αc1
The azimuth angles from the observation gravity center point to each observation point are as follows:
α′c,i+1＝αc,i+βi
calculating the current observation coordinate in the reference circle:
Figure BDA0003196480440000141
setting: the reference i point is now located at (X)i 0,Yi 0) Azimuth angle α of movement amounti 0The displacement of the reference in the X direction is deltaxThe displacement amount in the Y direction is deltayThe reference rotation angle is deltaαThe coordinates of the i point after the change of the reference position are as follows: (X)i,Yi) Azimuthal angle of deformation amount of alphai. Amount v of deformation point i in X-direction and Y-directionxi，vyiRespectively as follows:
Figure BDA0003196480440000151
in the formula: xi＝Xi 0+δxι；Yi＝Yi 0+δyι；αi＝αi 0+δαiLinearization can give:
because the adjustment coordinate precision of each point is the same, then:
Figure BDA0003196480440000152
solving according to the least square principle:
Figure BDA0003196480440000153
Figure BDA0003196480440000154
Figure BDA0003196480440000155
obtaining the correct position of the reference:
Xi＝Xi 0+δxι；Yi＝Yi 0+δyι；αi＝αi 0+δαi(i＝1,2,…,n)
obtaining the displacement of each point in the longitudinal direction and the transverse direction:
Figure BDA0003196480440000156
calculating the displacement and azimuth angle of the observation point:
Figure BDA0003196480440000157
Figure BDA0003196480440000158
reference displacement amount calculation result: coordinate system rotation angle offset value: deltaα＝2.190049880668260000(d.ms)
Coordinate system longitudinal translation amount adjustment value: deltax＝0.000008001269604000(m)
Coordinate system lateral translation amount adjustment value: δ y becoming 0.000008449192839000(m)
Sum of squares of movement amounts: [ vv)]＝0.0005774426655794000(m2)
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A measurement adjustment method based on dynamic reference is characterized by comprising the following steps:
s1, arranging a plurality of datum points and observation points in the foundation pit to be monitored, wherein the datum points are arranged on the edge of the foundation pit in a curve manner;
s2, setting a reference point coordinate, and calculating to obtain the coordinate of the observation point by combining the direction angle and the distance between the reference point and the observation point and combining the gravity center coordinate and a difference method;
s3, when the foundation pit deforms, obtaining a plurality of deformed reference points, obtaining coordinates of the deformed reference points according to coordinates of the observation points, combining the distance and direction values of the observation points and the arbitrarily selected deformed reference points, combining a least square method, calculating to obtain coordinates of the deformed reference points, calculating to obtain the deformed reference coordinates and the reference coordinates in S1, and calculating a foundation pit displacement value.
2. The method of claim 1, wherein the observation point calculation in step S2 is as follows:
approximate coordinates in an arbitrary coordinate system: x is the number ofi″,yi″,i＝1,2,‥‥,n；
Direction observation value: l isi，i＝1,2,‥‥,3n；
Distance observation value: di，i＝1,2,‥‥,3n；
Obtaining a balance value by a balance method:
xi′＝xi″+δxi
yi′＝yi″+δyi
barycentric coordinates of the reference points:
Figure FDA0003196480430000011
Figure FDA0003196480430000012
in the formula: n is the number of points;
the barycentric coordinates of the reference points to the azimuth angle of the set reference points:
Figure FDA0003196480430000013
the center of gravity coordinates of the observation points are equal to the reference center of gravity coordinates:
xc＝Xc
yc＝Yc
the azimuth angle from the barycentric coordinate of the observation point to the set observation point is equal to the azimuth angle from the barycentric coordinate of the reference point to the set reference point:
α′c1＝αc1
obtaining the coordinates of the observation points:
Figure FDA0003196480430000021
3. the method of claim 1, wherein the adjustment method is specifically calculated as follows:
directional observation error equation:
vLi＝-δZ0+αiδx0+biδy0-aiδxi-biδyi-li
in the formula: a isi，biAre respectively the linearized coefficient, δx0，δy0Two translational amounts, δ, each being a dynamic referenceZ0A rotation amount that is a dynamic reference;
distance observation error equation:
vDi＝-cosαiδx0-sinαiδy0+cosαiδxi+sinαiδyi-lDi
in the formula: 12 … m, lDiIs a constant term, δx0、δy0Are respectively observation points, δxi，δy0Respectively as a sight point;
in the formula: 12 … 3 n;
coefficients of the normal equation:
NBB＝BT·P·B
in the formula: delta is a vector, B is a row vector, and l is a constant term;
constant term of the normal equation:
W＝BT·P·l
in the formula: b isTIs matrix transposition, P is a weight matrix, and B is a matrix without transposition;
the equation:
NBBδ-W＝0
obtaining:
NCCδ-W＝0
obtaining a balance value:
xi′＝xi″+δxi
yi′＝yi″+δyi。
4. the method for measuring adjustment based on dynamic reference as claimed in claim 1, wherein the specific calculation process in step S3 is as follows:
the amount v of deformation of the deformed reference point in the X direction and the Y directionxi，vyiRespectively as follows:
Figure FDA0003196480430000031
obtaining according to a least square method:
Figure FDA0003196480430000032
Figure FDA0003196480430000033
Figure FDA0003196480430000034
obtaining a foundation pit displacement value:
Figure FDA0003196480430000035
in the formula: δ is the vector, B is the row vector, and l is the constant term.
5. The method for measuring adjustment based on dynamic reference as claimed in claim 1, wherein the edge of the pit to be monitored in step S1 has a plurality of reference points, and the plurality of reference points may be distributed in a hyperbolic curve at the edge of the pit to be monitored.
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